The paper analyzes the price, output and welfare effects of third-degree price discrimination triggered by the portfolio motive of a risk-averse monopolist facing random and potentially correlated market demands. It is shown that contrary to conventional wisdom, price discrimination can occur with identical expected demands, the relatively inelastic but risky market may be charged the lower price and despite linear demands, aggregate expected output may fall but expected consumer and producer surplus may rise. These results are shown to be driven by the risk aversion of the monopolist and the asymmetry in the risk and revenue characteristics of the markets.